Geodesic
A Bernstein-type theorem for minimal graphs over convex domains
Annales de l'I.H.P. Analyse non linéaire, Tome 39 (2022) no. 3, pp. 749-760

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Given any n≥2, we show that if Ω⊊ℝ n is an open convex domain (e.g. a half-space), and u:Ω→ℝ is a solution to the minimal surface equation which agrees with a linear function on δΩ, then u must itself be linear.

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DOI : 10.4171/aihpc/18
Classification : 49Q05, 35A02, 35J25, 53A10
Keywords: Minimal graphs, Bernstein theorem, convex domain, Dirichlet boundary 
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     author = {Edelen, Nick and Wang, Zhehui},
     title = {A {Bernstein-type} theorem for minimal graphs over convex domains},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {749--760},
     volume = {39},
     number = {3},
     year = {2022},
     doi = {10.4171/aihpc/18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/18/}
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Edelen, Nick; Wang, Zhehui. A Bernstein-type theorem for minimal graphs over convex domains. Annales de l'I.H.P. Analyse non linéaire, Tome 39 (2022) no. 3, pp. 749-760. doi: 10.4171/aihpc/18

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